You you bought a house worth $328,000. You paid 25% of the purchase price in cash and arranged a 25 year mortgage with a rate of 4.0% compounded semi-annually for the remaining balance. The mortgage has an amortization period of 25 years. How much interest will you pay in the first 7 years (assuming that the first payment is made at the end of the first month)?
So far, I have that PV=$328,000 * 0.75=$246,000, r=0.00330589 (using effective rate formula: (1+r)^6=(1+0.04/2) ) and n=25 * 12=300. Using the present value of an ordinary annuity:
I solved for PMT and got PMT=$1294.009652 for the monthly payments. The number of payment periods still remaining after 7 years is 18*12=216. The PV of the outstanding balance (FV of 246,000 - FV of 84 PMTs) is $199,539.6457. However, I don't really know what to do after that. The correct answer is $62,236.46 but I don't know how they got that. How do I calculate the interest paid in the first 7 years?